English translation is second picture Exercise 3.1: A charged Illne havlng a constant llnear denslty A Is located between x = 0 anda = a, as shown in the figure. Determine the electric field E at the coordinate point P(a/4,a/2).yaFigure 1: Linear load distribution. Ejercicio 3.1: Una línea cargada que posee una densidad lineal constante A se ubica entre r = 0 ya = a, tal como se indica en la figura. Determine el campo eléctrico É en el punto P de coordenadas(a/4, a/2).yaFigura 1: Distribución lineal de carga.

Answered: Exerclse 3.1: A charged lne havlng a…

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English translation is second picture

Exercise 3.1: A charged Illne havlng a constant llnear denslty A Is located between x = 0 and
a = a, as shown in the figure. Determine the electric field E at the coordinate point P
(a/4,a/2).
y
a
Figure 1: Linear load distribution.

Ejercicio 3.1: Una línea cargada que posee una densidad lineal constante A se ubica entre r = 0 y
a = a, tal como se indica en la figura. Determine el campo eléctrico É en el punto P de coordenadas
(a/4, a/2).
y
a
Figura 1: Distribución lineal de carga.

Expert Solution

Step 1

The electric field is to be calculated at point (a/2,a/4)

$L i n e a r c h a r g e d e n s i t y = A = \frac{q}{a} L e t u s c o n s i d e r a s m a l l l e n g t h e l e m e n t d x a t a d i s \tan c e x f r o m t h e o r i g i n . L e t a n e w s y s t e m o f c a r t e s i a n a x e s c o o r d i n a t e s b e d e f i n e d s u c h t h a t t h e o r i g n b e s h i f t e d t o t h e o r i g i n a l m i d p o i n t w h i c h o f t h e c h a r g e d i s t r i b u t i o n a n d t h e l e n g t h e x t e n d s f r o m x = - a / 2 t o x = + a / 2, w i t h m i d p o i n t a t x = 0 (w h i c h w a s o r i g i n a l l y x = a / 2) T h e e l e c t r i c f i e l d i s g i v e n a s d E = \frac{1}{4 {πε}_{0}} \frac{d q}{r^{2}} r = d i s \tan c e f r o m d q t o t h e p o i n t P (w h e r e e l e c t r i c f i e l d i s t o b e f o u n d) d E = \frac{1}{4 {πε}_{0}} \frac{d q}{r^{2}} = \frac{1}{4 {πε}_{0}} \frac{A d x}{r^{2}}$

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Exerclse 3.1: A charged lne havlng a constant llnear denslty A Is located between x = 0 and a = a, as shown in the figure. Determine the electric field E at the coordinate point P (a/4,a/2). y a Figure inoar lead distributien